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A143150
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A triangle sequence based on the Folium of Descartes implicit: x^3+y^3-3*a*x*y: t(n,m)=n^3+m^3-3*n*m.
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0
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-1, 3, 4, 19, 17, 27, 53, 48, 55, 80, 111, 103, 107, 129, 175, 199, 188, 189, 208, 251, 324, 323, 309, 307, 323, 363, 433, 539, 489, 472, 467, 480, 517, 584, 687, 832, 703, 683, 675, 685, 719, 783, 883, 1025, 1215, 971, 948, 937, 944, 975, 1036, 1133, 1272, 1459, 1700
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums are:
{-1, 7, 63, 236, 625, 1359, 2597, 4528, 7371, 11375}.
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REFERENCES
| Smamuel M. Shelby, ed., "CRC Standard Mathematical Tables and Formulae", 12th Edition, Curves and Surfaces (page 421),
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FORMULA
| t(n,m)=n^3+m^3-3*n*m.
row sums: sum_{m=1..n} t(n,m) = n^2*(5n^2-4n-5)/4 . [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2008]
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EXAMPLE
| {-1},
{3, 4},
{19, 17, 27},
{53, 48, 55, 80},
{111, 103, 107, 129, 175},
{199, 188, 189, 208, 251, 324},
{323, 309, 307, 323, 363, 433, 539},
{489, 472, 467, 480, 517, 584, 687, 832},
{703, 683, 675, 685, 719, 783, 883, 1025, 1215},
{971, 948, 937, 944, 975, 1036, 1133, 1272, 1459, 1700}
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MATHEMATICA
| Clear[t, n, m]; t[n_, m_] = n^3 + m^3 - 3*n*m; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]
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CROSSREFS
| Sequence in context: A089427 A197564 A020344 * A100340 A042175 A041703
Adjacent sequences: A143147 A143148 A143149 * A143151 A143152 A143153
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KEYWORD
| uned,sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 17 2008
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